A study of symbolic description, numerical efficiency and accuracy of 2D and 3D contact formulations

摘要

Complex 3D contact formulations, including various types of smoothing, advanced friction laws and sensitivity analysis have become computationally progressively expensive and, for moderate size problems, can be the main obstacle for practical application of these formulations. The aim of the paper is to present a general symbolic description of contact problems and to study the efficiency and the accuracy of several formulations of contact finite elements. For the study to be comprehensive, an approach is needed that enables derivation of the required formulas (e.g. element residual and tangent), their finite element coding, and running of some benchmark problems in an objective way. This has been achieved by using a symbolic approach to derivation of formulas and automatic code generation.